Pechernyi V. Origin, Evolution and Disappearing of Determini- stic Chaos in Pendulum and Electorelastic Systems with Limited Excitation

In the thesis a complex of modeling tools of dynamic systems which allows to solve a problem of the research of deterministic chaos in vibrating systems with a limited power-supply is developed. In such system feedback influence of oscillation loading on excitation source leads to nonregular chaotic regimes of coupled system. For electroelastic and pendulum systems sufficient conditions of asymptotic stability for equilibrium states are determined and influence of limited excitation and system parameters is analyzed. For pendulum system existence of singular surface is proved and its formula is deduced. Maps of dynamical regimes which allows determine possible regular and chaotic regimes are constructed. Diagrams of Lyapunov's characteristic exponents and bifurcation trees of the systems, phase portraits, Poincare's sections and maps, distributions of spectral density and invariant measure of regular and chaotic attractors are constructed and investigated in details. For electroelastic system realizations of all main scenarios of transition to chaos such as intermittency, cascade bifurcations of period doubling and destruction of quasiperiodic regimes are revealed. For pendulum system qeneralized feature of transition to chaos through cascade bifurcations of period doubling is determined.